The document discusses strategies for promoting algebraic thinking. It presents an activity using M&Ms to model decay, describes using tiles to model functions, and discusses using spreadsheets to model relationships. Spreadsheets allow students to explore concepts through algebraic, tabular, and graphical representations. The document emphasizes that multiple representations give students powerful tools for success in mathematics.

1. Strategies and Practices to
Promote Algebraic Thinking
Reva Narasimhan
Associate Professor of Mathematics
Kean University
www.mymathspace.net

2. Algebraic Thinking
• Many students struggle with developing generalizations for
functional relationships
• Bridge the gap between their concrete experiences in prior
mathematics courses and the abstract symbolic work in later
courses
• Students need help to make sense of this increasing abstraction
• By developing students’ facility in using multiple representations
you give them a powerful tool for success in advanced
mathematics.
Reva Narasimhan
www.mymathspace.net

3. M&M activity on decay
1. Count how many total M&M’s there are in your
packet. This is the initial value.
2. Shake up M&M’s and drop the candies on a piece of
paper.
3. Count how many have “m” on top
4. Record on paper.
5. Remove these candies and repeat Steps 2-4 until no
candies with “m” on top appear
6. Record results in Excel spreadsheet and model the
behavior.
Reva Narasimhan
www.mymathspace.net

4. Tiling the Border of a Pool
Source: http://ccsstoolbox.agilemind.com/animations/functions_3.html
Reva Narasimhan
www.mymathspace.net

5. Minimizing Cost
Consider the problem of
designing the most costefficient cylindrical juice can
that holds 20 cubic inches of
soda.
This problem requires
students to bring together
understanding of surface
area and volume, and ability
to use variables to represent
geometric relationships
Reva Narasimhan
www.mymathspace.net
Source: http://ccsstoolbox.agilemind.com/animations/functions_5.html

6. Technology and Algebraic Thinking
A spreadsheet can be a powerful ally
in facilitating algebraic thinking
Reva Narasimhan
www.mymathspace.net

7. Summary of Spreadsheets
• A spreadsheet can be used to unify algebraic, tabular and graphical
representations of an abstract concept.
• Gives valuable insight which may not be gained by just pencil and paper
work.
• Shows students the power of technology to explore and make conjectures
which would otherwise be very difficult or impossible.
• Helping students build such insight is invaluable as they move on to other
courses and their professions.
Reva Narasimhan
www.mymathspace.net

8. Algebraic Concepts and Connections
What comes to your mind
at the mention of algebra?
Reva Narasimhan
www.mymathspace.net

9. Reva Narasimhan
www.mymathspace.net

10. Dynamic geometry – move it
and see it
Visual and tactile
What does the algebra
problem look like in
GeoGebra?
Reva Narasimhan
www.mymathspace.net

11. Reva Narasimhan
www.mymathspace.net

12. GeoGebra vs Graphing Calculator
The ability to interact dynamically with a graph
sets GeoGebra apart from many other
graphing software and calculators
Reva Narasimhan
www.mymathspace.net

13. What is GeoGebra?
• Free and open source software created Markus Hohenwarter of
Austria
www.geogebra.org
• A multi-platform dynamic mathematics software that joins
geometry, algebra, tables, graphing, statistics and calculus in one
easy-to-use package.
Reva Narasimhan
www.mymathspace.net

14. What is GeoGebra?
Graphics, algebra and tables are connected
and fully dynamic
Can easily create interactive learning
materials as web pages
Reva Narasimhan
www.mymathspace.net

15. Solution of Equations
• Relate algebraic representation to graphical representation
• Recast an equation as an intersection of the graphs of two functions
• Explore nature of solutions
Reva Narasimhan
www.mymathspace.net

16. Summary
• Multistep applications hold student interest and
get them to connect with the mathematics they
are learning.
• New algebraic skills that are introduced are now
in some context.
• Gives some rationale for why we define
mathematical objects the way we do.
Reva Narasimhan
www.mymathspace.net

17. Contact Information
• Web:
http://www.mymathspace.net/presentations
Reva Narasimhan
www.mymathspace.net